1. Field of the Invention
The present invention relates to a fault location method of a single fault or multiple faults of a parallel two-circuit transmission line with n terminals.
2. Discussion of the Related Art
Electric power is usually transmitted between electric power substations by the use of a parallel two-circuit transmission line. This transmission line is subject to various types of faults due to external factors (e.g. insulation breaks due to lightning strikes or contacts with birds or trees). Most of the faults are single phase groundings. A fault-locating operation is used where locating the fault by inspection is difficult, such as in mountainous regions. The types of faults include (1) a fault at one location on one circuit, (2) faults at different locations on one circuit, (3) faults at the same location on both circuits, (4) faults at different locations on the two circuit. Faults of type (1) are generally said to be a "single fault" and represent the majority of faults. Faults of types (2)-(4) are referred to as multiple faults, the majority of which are of type (3). The present invention relates to faults of types (1) and (3).
A variety of ground fault location have been proposed. For example, a type (1) fault may be located with a method in which zero-phase currents I.sub.01 and I.sub.02 of the respective circuits of a two-terminal parallel two-circuit transmission line are detected to produce a shunt current ratio of the zero-phase currents defined by: EQU 2I.sub.01 /(I.sub.01 +I.sub.02) where i=1 or 2,
and the distance from the sending end to a single phase ground fault is calculated on the basis of the shunt current ratio of the zero-phase currents and the total length of the transmission line.
FIG. 8 illustrates the above-described method. A Y-.DELTA. transformer c is disposed with its neutral point grounded via a high resistance b at a sending end a, and a Y-.DELTA. transformer e without grounding is disposed at a receiving end d. The transformers c and e are connected to bus lines g1 and g2, respectively, between which f1 and f2 of a two-circuit transmission line having a length l are connected. FIG. 9 shows a zero-phase equivalent circuit of FIG. 8, where the zero-phase current of the circuit f1 is I.sub.01, the zero-phase current of the circuit f2 is I.sub.02, the zero-phase voltage of the bus g1 is Vo, the zero-phase voltage of the ground fault point is Vof, the zero-phase-sequence impedance per unit length is Z.sub.o, and the zero sequence mutual impedance between the circuits is Z.sub.m.
With the aforementioned parallel two-circuit transmission line, we assume that a single phase ground fault occurs at a distance x from the sending end and a ground fault current I.sub.0f is flowing from the fault point to the ground. The distance x can be determined by calculating the zero-phase current ratio. That is, the single phase ground fault point can be located on the basis of only the zero-phase currents I.sub.01 and I.sub.02 of the circuits f1 and f2, respectively. The above-mentioned single phase ground fault calculation method is an easy way of locating the fault because the distance from the sending end to the ground fault point is calculated only on the basis of the shunt current ratio of the zero-phase currents detected from the respective circuits. However, this method cannot be directly applied to the fault localization of a single phase ground fault in a three-terminal system where the transmission circuits are branched such that one end of each branch is loaded.
A fault-localization method such that by the use of the shunt current ratio of the zero-phase currents a fault point which occurs in a single phase of a parallel two-circuit transmission line with three terminals in a resistor grounded neutral system can be located has been proposed in Japanese Patent Application No. 63-169739. In this method, correction factors are precalculated based on the distance from the sending end to a single phase ground fault point so that the distance from the sending end to the ground fault point is calculated, or correction factors are precalculated based on the distance from a branch of the two-circuit transmission line to a single phase ground fault point so that the distance from the branch to the ground fault point is calculated.
However, this method utilizes only the information from the sending one end, thus, may only be applied to the simple faults of type (1).
A method of fault-localization for a two-terminal parallel two-circuit transmission line in a resistance grounded neutral system and for a three-terminal parallel two-circuit transmission line has been proposed in Japanese Patent Application No. 63-307612.
In this method, the zero-phase equivalent circuit of a three-terminal parallel two-circuit transmission line of the resistance grounded neutral system is first analyzed, and then the zero-phase equivalent circuit is transformed into an equivalent circuit in terms of the zero-phase difference currents (referred to as a difference current equivalent circuit hereinafter). This method is described below.
FIG. 10A shows a three-terminal parallel two-circuit transmission line where l.sub.a is a distance from the sending end to a branch point, and l.sub.b and l.sub.c are distances from the branch point to two receiving ends. The distances l.sub.a, l.sub.b, and l.sub.c are the lengths of the transmission lines and are known. FIG. 10B shows a zero-phase equivalent circuit of the aforementioned three-terminal parallel two-circuit transmission line and FIG. 10C shows a difference-current equivalent circuit derived on the basis of the zero-phase current difference of the respective circuits.
In FIG. 10C, .DELTA.I.sub.0a is the difference current flowing into the branch point from the sending end A, .DELTA.I.sub.0b and .DELTA.I.sub.0c are the difference circuits flowing into the branch point from receiving ends B and C, respectively, and .DELTA.I.sub.0f is the difference current flowing out of the single phase ground fault. When a single phase ground fault occurs between the sending end A and the branch point, the shunt current ratio of zero-phase difference current is given by ##EQU1## Using the above equation, the following relationship is obtained: ##EQU2## where L=l.sub.a l.sub.b +l.sub.b l.sub.c +l.sub.a l.sub.c.
When x is greater than l.sub.a, that is, when the single ground fault occurred at a point on the line farther from the sending point A than the branch point is from sending point A, the shunt current ratio of the zero-phase difference currents is given by ##EQU3## Using this relation, the distance x from the receiving end C to the fault is calculated by ##EQU4## If x is smaller than l.sub.c, then x is the distance from the receiving end C to the ground fault (refer to FIG. 10D).
When x is greater than l.sub.c, then the shunt current ratio of zero sequence differential current is given by ##EQU5##
By the use of this relation, the distance x from the receiving and B to the fault is calculated by ##EQU6## If x is smaller than l.sub.b, then x is the distance from the receiving end B to the ground fault (refer to FIG. 10E).
Thus, the zero-phase currents of the respective circuits at the sending end A and the receiving ends B and C are detected and the shunt current ratios of the zero sequence differential current are then multiplied by correction factors given by L(l.sub.b +l.sub.c), L/(l.sub.c +l.sub.a), and L/(l.sub.a +l.sub.b) respectively, thus providing the distance x from each end to the single phase fault.
Another conventional method of short-circuit localization is on the principle of a 44S relay calculation operation where the impedance from a sending end to a fault point is determined by dividing a line delta voltage, line delta current when a fault occurs. FIG. 11 is a simplified circuit diagram of a three-terminal parallel two-circuit transmission line, illustrating the above-described 44S method. In this figure, circuits f1 and f2 are connected between a sending end A and a receiving end B having a two-circuit branch point T from which the circuit f1 and f2 branch off to a receiving end D. A load LB is connected with the receiving end B and a load LC with the receiving end C. In the circuit, x is a distance from the sending end A to a fault point in FIG. 11A or a distance from the branch point T to a fault point in FIGS. 11B and 11C; l.sub.a is a distance from the sending end A to the two-circuit branch point T; l.sub.b is a distance between the two-circuit branch point T and the receiving end B; l.sub.c is a distance between the two-circuit branch point T and the receiving end C; Z is a positive sequence impedance per unit length of the transmission line; Va and Vb are voltages of phases A and B, respectively, at the sending end A; Vaf and Vbf are voltages of phases A and B, respectively, at a fault point; I.sub.a1 and I.sub.b1 are currents of phases A and B of the circuit f1 at the sending end A; I.sub.a1 ' and I.sub.b1 ' are currents of phases A and B of the circuit f1 at the receiving end B; I.sub.a1 " and I.sub.b1 " are currents of phases A and B of the circuit f1 at the receiving end C; I.sub.LBa and I.sub.LBb are currents of phases A and B flowing into the load LB when a fault occurs; and I.sub.LCa and I.sub.LCb are currents of phases A and B flowing into the load LC when a fault occurs.
With the aforementioned condition, by the use of the 44S method algorithm, a distance x is determined for (1) a short-circuit in which the phase A is short-circuited to the phase B of the circuit f1 between the sending end A and the two-circuit branch point T (FIG. 11A), (2) a short-circuit in which the phase A is short-circuited to the phase of the B of the circuit f1 between the receiving end B and the two-circuit branch point T (FIG. 11B), and (3) a short-circuit in which the phase A is short-circuited to the phase B of the circuit f1 between the receiving end C and the two-circuit branch point T (FIG. 11C).
For the case (1), the following equation is derived using Kirchhoff's voltage low: EQU V.sub.af -V.sub.bf =V.sub.a -V.sub.b -xZ(I.sub.a1 -I.sub.b1).
Rewriting the above equation, we have: EQU (V.sub.a -V.sub.b)/(I.sub.a1 -I.sub.b1)=xZ+(V.sub.af -V.sub.bf)/(I.sub.a1 -I.sub.b1)
For the case (2), the following equation is derived by again using Kirchhoff's voltage low: EQU V.sub.af -V.sub.bf =V.sub.a -V.sub.b -(l.sub.a +x)Z(I.sub.a1 -I.sub.b1)-xZ(I.sub.a1 "-I.sub.b1 ")
Rewriting the above equation, we have ##EQU7## Likewise, for the case (3), the following equation is obtained. ##EQU8##
As is apparent from above, the three equations include the positive sequence impedance to the fault point for the first term on the right hand side, as well as an error (Vaf-Vbf)/(I.sub.a1 -I.sub.b1) of the fault point due to a fault resistance, and errors xZ(I.sub.a1 "-I.sub.b1 ")/(I.sub.a1 -I.sub.b1) or xZ(I.sub.a1 '-I.sub.b1 ')/(I.sub.a1 -I.sub.b1) due to shunt current through a parallel line and a sound branch.
The value of (Vaf-Vbf) is small when a short-circuit fault occurs, and (I.sub.a1 -I.sub.b1) includes the short-circuit current and the load current. The load current may be neglected. Thus, (Vaf-Vbf)/(I.sub.a1 -I.sub.b1) is considered to be a resistance at a fault. Accordingly, by adopting the reactance component, the effects thereof can be nearly eliminated. The distance x to a fault point in the above case (1) can be calculated through the following equation. EQU I.sub.m [(V.sub.a -V.sub.b)/I.sub.a1 -I.sub.b1)]=x I.sub.m [Z]
where I.sub.m [. . . ] is the reactance component.
However, a branch error is caused by the fact that the fault current is distributed to the two-circuit branches as in the cases (2) and (3). A fault location method free from the effects of the branch error has been proposed (Japanese Patent Application No. Sho. 63-307612).
The aforementioned methods of fault-localization for three-terminal parallel two-circuit transmission lines are capable of localizing a ground fault on three-terminal parallel two circuit transmission lines, but cannot be applied to parallel two-circuit transmission lines having more than three terminals. In recent years, the parallel two-circuit transmission lines have often been of multiterminal systems, and there has been a need for a ground fault localization method that can generally be applied to n-terminal parallel two-circuit transmission lines.
Today, sophisticated methods have been employed for protecting the parallel two-circuit transmission lines. An example of such a method is the differential current protection method where current information at the respective terminals are transmitted to the main station by means of radio transmission or optical transmission, so that the fault localization may be performed on the basis of the current information at all the terminals.